Stress-induced anisotropy in solids—the acousto-elastic effect

Smith, R. T.

doi:10.1016/0041-624x(63)90003-9

Cited by 73 publications

(20 citation statements)

References 29 publications

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“…The first back echo may not show sufficient interference to permit observation but after several transits, the phase difference can increase to half a wavelength, thus causing the cancellation of an echo and consequently the echo sequence shows beats. It is also possible to connect in the lead of one of the two transducers an electric phase control [380,378,659,1287,1288,1437,1160, 243J.…”

Section: Measurement Of Sound Velocity and Stressmentioning

confidence: 99%

Ultrasonic Testing of Materials

Krautkrämer¹,

Krautkrämer²

1990

789

452

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Section: Measurement Of Sound Velocity and Stressmentioning

confidence: 99%

Ultrasonic Testing of Materials

Krautkrämer¹,

Krautkrämer²

1990

789

452

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“…Acoustoelastic effects refer to the changes in the elastic wave velocities related to stress‐induced effects. It has been theoretically explained for a Green elastic or hyperelastic medium, that is, an elastic medium where stresses depend only on the current state of deformation (Smith, ). In this case, the stored elastic energy per unit of undeformed volume W elas is a polynomial function of the strain tensor ε :

W_{elas} ()(, ε) = \frac{1}{2} {C^{()(, 2)}}_{ijkl} ε_{ij} bold ε_{kl} bold + \frac{1}{6} {C^{()(, 3)}}_{ijklmn} ε_{ij} bold ε_{kl} bold ε_{mn} + \dots,

where the coefficients in C (2) ijkl are the second‐order elastic constants and in C (3) ijklmn the third‐order elastic constants (TOEC) (Smith, ; Toupin & Bernstein, ).…”

Section: Cwi Monitoringmentioning

confidence: 99%

Elastic Strain Effects on Wave Scattering: Implications for Coda Wave Interferometry (CWI)

et al. 2020

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Coda Wave Interferometry (CWI) is a highly sensitive monitoring technique built on the sensitivity of elastic coda waves to small changes in a diffusive medium. However, a clear connection between the physical processes involved in the evolution of the medium and the time changes observed by CWI has not been clearly described yet. Here, we quantify the impact of elastic deformation on CWI measurements at laboratory scales. We compare experimental results from wave scattering measurements during a uniaxial compression test to those of a numerical approach based on the combination of two codes (SPECFEM2D and Code_Aster), which allows us to model wave propagation in complex diffusive media during its elastic deformation. In both approaches, the reversible time delays measured between waveforms increase with the elastic deformation of the sample. From the numerical modeling, we gain insight to the relative contributions of different physical effects on the CWI measurement: local density changes from volumetric strain, the deformation of scatterers, and acoustoelastic effects. Our results suggest that acoustoelastics effects related to nonlinear elasticity are dominant.

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“…The bulk modulus and elasticity modulus of the material are commonly available. However, third order elastic constants are usually obtained by experiments [10,12,13]. In this work acoustoelastic constant Lzz for bearing steel was determined by experiment to be Lzz = -2.24(see Appendix).…”

Section: Acoustoelastic Effectmentioning

confidence: 99%

Direct load monitoring of rolling bearing contacts using ultrasonic time of flight

2015

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The load applied by each rolling element on a bearing raceway controls friction, wear, and service life. It is possible to infer bearing load from load cells or strain gauges on the shaft or bearing housing. However this is not always simply and uniquely related to the real load transmitted by rolling elements directly to the raceway. Firstly, the load sharing between rolling elements in the raceway is statically indeterminate. And secondly, in a machine with nonsteady loading the load path is complex and highly transient being subject to dynamic behavior of the transmission. This study describes a method to measure the load transmitted directly by a rolling element to the raceway by using the time of flight (ToF) of a reflected ultrasonic pulse.A piezoelectric sensor was permanently bonded onto the bore surface of the inner raceway of a cylindrical roller bearing. The time of flight of an ultrasonic pulse from the sensor to the roller-raceway contact was measured. This depends on the speed of the wave and the thickness of the raceway. The speed of an ultrasonic wave changes with the state of the stress; known as the acoustoelastic effect. The thickness of the material varies when deflection occurs as the contacting surfaces are subjected to load. In addition, the contact stiffness changes the phase of the reflected signal and in simple peak to peak measurement, this appears as a change in the ToF. In this work the Hilbert transform was used to remove this contact dependent phase shift.Experiments have been performed on both a model line contact and a single row cylindrical roller bearing from the planet gear of a wind turbine epicyclic gearbox. The change in ToF under different bearing loads was recorded and used to determine the deflection of the raceway. This was then related to the bearing load using a simple elastic contact model. Measured load from the ultrasonic reflection was compared with the applied bearing load with good agreement. The technique shows promise as an effective method for load monitoring in real bearing applications.

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Stress-induced anisotropy in solids—the acousto-elastic effect

Cited by 73 publications

References 29 publications

Ultrasonic Testing of Materials

Ultrasonic Testing of Materials

Elastic Strain Effects on Wave Scattering: Implications for Coda Wave Interferometry (CWI)

Direct load monitoring of rolling bearing contacts using ultrasonic time of flight

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